Models of biological pattern formation in space and time


Hans Meinhardt

Max-Planck-Institute for Developmental Biology, Spemannstrs. 35, D-72076, Tübingen, Germany. 


Euresis Journal, volume 7 (2014), pages 27-46

The role of time in the development of higher organisms is obvious. Starting with a single cell, development requires a chain of linked pattern-forming processes. In biology, all processes are achieved by the interaction of molecules. Pattern formation in space requires that local concentration maxima emerge from originally more or less homogeneous initial distributions. Such maxima act as signaling centers, i.e., as organizing regions, instructing the surrounding cells to allow a position-specific behaviour. Spatial patterns are generated by reactions in which particular molecules have a strong positive feedback on their own production rate. This self-enhancing reaction has to be balanced by a more rapidly spreading antagonist. The theoretically predicted interactions found full support by more recent observations on the molecular-genetic level. If the antagonistic reactions have a longer time constant, the same type of interactions can also lead to patterns in time, including sustained oscilations, spike-like activations and travelling waves. These mechanisms are universal and drive also pattern formation in the non-animated world, for instance, in the formation of sand dunes, lighting, or in the ups and downs of the stock maket.